Rotations
How do you find the new image of a point after a 90 degree clockwise rotation?
switch, negate second
Define a reflection
A reflection flips a given image over a line
Define a translation
A translation is when you slide an image a particular distance
A dilation enlarges or decreases an image's size
What are the four types of transformations?
Rotations, Reflections, Dilations, Translations
Define a rotation
A transformation around a fixed point
If you reflect over the x-axis, which coordinate changes its value - the x or the y?
The y!
Are the image and pre-image congruent or similar in a translation?
congruent
What is the scale factor?
The scale factor is the number to multiply by
Given the point (1,2), what is its image after a reflection over the x-axis, then a dilation of 4?
(4,-8)
Given the pre-image of the point (2,3), what is the image after a 270 degree clockwise rotation?
(-3,2)
If the pre-image is (4,1) and the image is (-4,1), what line is this point reflected over?
The y-axis
What properties are preserved in translations?
Orientation, isometry, angle measure
How do you determine the ratio of the length of line segments in a dilation?
image/pre-image
Two transformations are performed on a figure on a coordinate plane. The first transformation is a translation 8 units to the left. What second transformation would result in an image that is similar to, but not congruent to, the original figure?
A dilation
Given the pre-image of the point (4,-5), what it its image after a 270 degree counterclockwise rotation?
(-5,-4)
Given the point (6,4), what is its image after a reflection over the x-axis?
(6,-4)
Given the point (-3,-7), what is its image after a translation 1 unit up and two units to the right?
(-1,-6)
What property is NOT preserved in a dilation?
isometry
Given the point (-5,3), what is the image after a rotation 180 degrees, then reflection over the y-axis?
(-5,-3)
Given Triangle ABC with coordinates (-3,1), (-3,7), (-6,7), What are the coordinates of Triangle A'B'C' after a 90 degree clockwise rotation? Also, which quadrant is Triangle A'B'C' in?
Triangle A'B'C' lies in Quadrant 1. Its coordinates are (1,3), (7,3), (7,6).
Given Square WXYZ, with coordinates (2,2), (4,2), (2,4), (4,4), what are the coordinates of Square W'X'Y'Z' after a reflection over the x-axis, and then a reflection over the y-axis?
(-2,-2), (-4,-2), (-2,-4), (-4,-4)
Given Triangle JKL with coordinates (3,-2), (5,-2), (5,-5), what is the image of Triangle J'K'L' after a translation 2 units left and 3 units up?
(1,1), (3,1), (3,-2)
Given Triangle QRS with coordinates (3,3), (3,6), (6,6), what is its image after dilating by 1/3?
(1,1), (1,2), (2,2)
Given the point (3,6) and its image (-1,-2), describe the series of transformations on the point (3,6) that would result in the point (-1,-2)
Dilation of 1/3, then rotation of 180 degrees